Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1192 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×#890 | C2 | direct (N × H) |
| 18. #890 | C22 | direct (N × H) |
| 82. C22×C3 | #125 | semidirect |
| 106. C2×C3 | C2×#125 | semidirect |
| 110. C22 | #890 | direct (N × H) |
| 120. C3 | C22×#125 | semidirect |
| 121. C2 | C2×#890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×Dic3⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| C2×#890 | 2 |
| C22×#125 | 3 |